NKA
Nonlinear Krylov acceleration of fixed-point and Newton-like methods
... it has gleaned from previous solution iterates.
It was only recently recognized (2011) that NLK is essentially equivalent to Anderson Acceleration for a specific choice of mixing parameter. NLK was independently devised in the late 1980's using a very different approach, and though it leads to the same algebraic method, NLK's organization is somewhat different, and arguably superior. The NLK approach also provides clear rationale for the proper choice of Anderson's arbitrary mixing parameter.